Question

Given the functions j(x) = x2 − 9 and k(x) = −x2 + 7x − 1, which operation results in a 3rd degree polynomial?

Answer 1

1.] multiplication of x squared by x yields a 3rd degree polynomial (having an x cubed term) 

2.] (x+3)^1/2 - 4 = x - 1 
(x+3)^1/2 = x + 3 
square both sides: x+3 = (x+3)^2 
simplify: x + 3 = x^2 + 6x + 9 
bring all terms to one side so that 0 = x^2 + 5x + 6 
factor the polynomial 0 = (x + 2) ( x + 3) 
set each factor equal to zero & solve to get x = -2 and x = -3 

3.] x = 4 , not extraneous 

4.] In mathematics, complex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of equal magnitude and opposite signs. So -6 - 5i and -6 + 5i are complex conjugates. 

5.] x = 8 and x = 9 

6.] x to the sixteenth twenty fifth power 
x^4/5 * x^4/5 multiply exponents to get x^16/25 

7.] quantity of 80 minus 50 i over 39